I'm adding a utility sink in my garage. To vent the drain, I'd like to connect into the vent pipe running up vertically from the kitchen sink drain pipe.

I've heard that I need to connect into the vent at least 6" above the flood level of the sink. Why is this minimum height required? I can easily tap into the vent pipe behind the dishwasher, but that means I will connect to the vent pipe about 2" below the flood level of the sink. Connecting any higher would require heavy drilling and tearing into visible portions of the kitchen wall.

How big of a risk would I be taking if I connected it lower than the 6" requirement? If that's unacceptable, any other suggestions? Thanks in advance.